Present study concerned with the theoretical work with numerical investigation of MHD transient naturally convective and higher order chemically reactive viscoelastic fluid with nano-particle flow through a vertical porous stretching sheet with the effects of heat generation and radiation absorption. A boundary layer approximation is carried out to develop a flow model representing time dependent momentum, energy, and concentration equations. The governing model equations in partial differential equations (PDEs) form were transformed into a set of nonlinear ordinary differential equation (ODEs) by using non-similar technique. Explicit Finite Difference Method (EFDM) was employed by implementing an algorithm in Compaq Visual Fortran 6.6a to solve the obtained set of nonlinear coupled ODEs. For optimizing the system parameter and accuracy of the system, the stability and convergence analysis (SCA) was carried out. It was observed that with initial boundary conditions, for 0.005

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Microbes swimming in a fluid that contains nanoparticles is an intriguing characteristic having ramifications in biomedicine, petroleum science, biofuels, and biotechnology applications. This study gives a theoretical evaluation of the bioconvection phenomena with swimming microorganisms in a Prandtl-Erying nanofluid constructed by an exponential stretched surface, given the amazing applications of bioconvection and nanoparticles. Additionally, the problem is modeled by considering intriguing phenomena such as thermophoretic particle deposition, Darcy-Forchheimer medium, exothermic/endothermic process, and activation energy vitality.The leading problem comprises nonlinear, coupled, partial differential expressions. To run the appraisal process, the controlling problem is transfigured into dimensionless patterns through the usual transformations. A computational finite difference approach is used to quantify the numerical evaluation of fabricated flow problems. To obtain the parametric constraints, stability and convergency were also assessed. Improved visualizations (streamlines, isothermal line, iso-concentration,

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